- RFunction

- Models > Function

- Name of the object in Rt.
- Allowable characters include upper-case and lower-case letters, numbers, and underscore (“_”).
- The name is unique and case-sensitive.

- Indicates the expression of the limit state function, for example:

1.0 - x2/(1000.0*x3) - (x1/(200.0*x3))^2

- The following functions can be used in the expression of the function:

Name | No. of Arguments | Explanation |
---|---|---|

sin | 1 | sine function |

cos | 1 | cosine function |

tan | 1 | tangent function |

asin | 1 | arcus sine function |

acos | 1 | arcus cosine function |

atan | 1 | arcus tangent function |

sinh | 1 | hyperbolic sine function |

cosh | 1 | hyperbolic cosine |

tanh | 1 | hyperbolic tangent function |

asinh | 1 | hyperbolic arcus sine function |

acosh | 1 | hyperbolic arcus cosine function |

atanh | 1 | hyperbolic arcus tangent function |

log2 | 1 | logarithm to the base 2 |

log10 | 1 | logarithm to the base 10 |

log | 1 | logarithm to the base 10 |

ln | 1 | logarithm to base e (2.71828...) |

exp | 1 | e raised to the power of x |

sqrt | 1 | square root of a value |

sign | 1 | sign function -1 if x<0; 1 if x>0 |

rint | 1 | round to nearest integer |

abs | 1 | absolute value |

if | 3 | if ... then ... else ... |

min | var. | min of all arguments |

max | var. | max of all arguments |

sum | var. | sum of all arguments |

avg | var. | mean value of all arguments |

- The following operators can be used in the expression of the function:

Operator | Meaning | Priority |
---|---|---|

= | assignment | -1 |

and | logical and | 1 |

or | logical or | 1 |

xor | logical xor | 1 |

<= | less or equal | 2 |

>= | greater or equal | 2 |

!= | not equal | 2 |

== | equal | 2 |

> | greater than | 2 |

< | less than | 2 |

+ | addition | 3 |

- | subtraction | 3 |

* | multiplication | 4 |

/ | division | 4 |

^ | raise x to the power of y | 5 |

- Indicates the methods to compute the gradient of the limit-state function, including finite difference method and direct difference method.
- For more information, see Zhang-Der Kiureghian (1993) and Kleiber (1997)

- The forward finite difference estimate of gradient vector for each variable is equal to its standard deviation divided by Perturbation Factor which is typically set equal to 1000.

- Efficient perturbation restricts Rtx to use perturbed values only for the models that are affected by variables' changes to recalculate function value. Two options are available: if the option “True” is set, program will run models affected by perturbation recognized by Rt, and in case the “False” option is set, the program will run all models for each perturbation.

- The current value of function as the results of calculations

- Limit-state function

- Removes the object.

- Zhang, Y., & Der Kiureghian, A. (1993). Dynamic response sensitivity of inelastic structures. Computer Methods in Applied Mechanics and Engineering, 108(1), 23–36
- Kleiber, M. (1997). Parameter sensitivity, J. Willey & Sons Ltd., Chichester